Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10: 0134467795
ISBN 13: 978-0-13446-779-5

Chapter 2 - Multiplying and Dividing Fractions - 2.3 Factors - 2.3 Exercises - Page 131: 54


All primes except 2 must be odd (otherwise they would be divisible by 2). Some odd numbers are not prime (e.g. 15).

Work Step by Step

Prime numbers are defined as (a) whole and (b) only divisible (evenly) by themselves and 1. For example, the numbers $3$, $5$, and $7$ are prime because they have no factor aside from themselves and 1. It is true that all prime numbers are odd, except for 2. This is because any even number would be divisible by itself, 1, and the number 2 (and hence would not be prime). But it does not follow that odd numbers are prime. This is because two prime numbers can multiply to an odd number that is then not prime. For example, $3$ and $5$ are prime. However, if you multiply them, you get $15$, which is odd, but not prime (because it is divisible by $15$, $1$, $3$, and $5$).
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